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An algorithm is proposed to calculate traveling dissipative solitons for theFitzHugh-Nagumo equations. It is based on the application of the steepestdescent method to a certain functional. This approach can be used to findsolitons whenever the problem has a variational structure. Since the methodseeks the lowest energy configuration, it has robust performance qualities. Itis global in nature, so that initial guesses for both the pulse profile and thewave speed can be quite different from the correct solution. Also, bifurcationshave a minimal effect on the performance. With an appropriate set of physicalparameters in two dimensional domains, we observe the co-existence ofsingle-soliton and 2-soliton solutions together with additional unstabletraveling pulses. The algorithm automatically calculates these various pulsesas the energy minimizers at different wave speeds. In addition to findingindividual solutions, this approach could be used to augment or initiatecontinuation algorithms.

A global algorithm for the computation of traveling dissipative solitons